• TITLE: H2-Optimal model reduction with higher-order poles
• AUTHORS: Paul Van Dooren, Kyle A. Gallivan, P.-A. Absil
• ABSTRACT:
  We consider the problem of approximating a multiple-input multiple-output (MIMO) $p\times m$ rational transfer function $H(s)$ of high degree by another $p\times m$ rational transfer function $\hH(s)$ of much smaller degree, so that the $\calH_2$ norm of the approximation error is minimized. We characterize the stationary points of the $\calH_2$ norm of the approximation error by tangential interpolation conditions and also extend these results to the discrete-time case. We analyze whether it is reasonable to assume that lower-order models can always be approximated arbitrarily closely by imposing only first-order interpolation conditions. Finally, we analyze the $\calH_2$ norm of the approximation error for a simple case in order to illustrate the complexity of the minimization problem.
• KEY WORDS: Multivariable systems, model reduction, optimal $\calH_2$ approximation, tangential interpolation
• STATUS: SIAM Journal on Matrix Analysis and Applications, 31(5), pp. 2738-2753, 2010

• Publisher's version: http://dx.doi.org/10.1137/080731591 [local copy]

BibTeX citation:

@ARTICLE{DooGalAbs2010,
  author = "Paul Van Dooren and Kyle A. Gallivan and P.-A. Absil",
  title = "H2-Optimal model reduction with higher-order poles",
  journal = "SIAM J. Matrix Anal. Appl.",
  fjournal = "SIAM Journal on Matrix Analysis and Applications",
  year = 2010,
  volume = 31,
  number = 5,
  pages = "2738-2753",
  doi = "10.1137/080731591",
}